# AP Calculus AB

# Calculator Policy

You can use a graphing calculator on Section I, Part B and Section II, Part A of the AP Calculus AB Exam since questions in those parts of the exam require use of the calculator to answer. See the list of approved graphing calculators (which includes a list of devices that are not allowed).

Bring a calculator you are familiar with. It is a good idea to bring extra batteries. You may bring up to two graphing calculators.

Throughout the course, use your calculator on a regular basis so that you’re comfortable with it on exam day.

**Graphing Calculator Capabilities**

A graphing calculator appropriate for use on the exam is expected to have the built-in capability to:

- Plot the graph of a function within an arbitrary viewing window
- Find the zeros of functions (solve equations numerically)
- Numerically calculate the derivative of a function
- Numerically calculate the value of a definite integral

The AP Program ensures that the exam questions do not favor students who use graphing calculators with more extensive built-in features.

**Showing Work on the Free-Response Sections**

You are expected to show enough of your work for AP Readers, the high school teachers and college faculty that are scoring the AP Exams, to follow your line of reasoning. To obtain full credit for the solution to a free-response problem, communicate your methods and conclusions clearly. Answers should show enough work so that the reasoning process can be followed throughout the solution. This is particularly important for assessing partial credit. You may also be asked to use complete sentences to explain or justify your methods or the reasonableness of your answers, or to interpret your results.

For results obtained using one of the four required calculator capabilities listed above, you are required to write the setup (e.g., the equation being solved, or the derivative or definite integral being evaluated) that leads to the solution, along with the result produced by the calculator. For example, if you are asked to find the area of a region, you are expected to show a definite integral (i.e., the setup) and the answer. You need not compute the antiderivative; the calculator may be used to calculate the value of the definite integral without further explanation. For solutions obtained using a calculator capability other than one of the four required ones, you must also show the mathematical steps that lead to the answer; a calculator result is not sufficient. For example, if you are asked to find a relative minimum value of a function, you are expected to use calculus and show the mathematical steps that lead to the answer. It is not sufficient to graph the function or use a built-in minimum finder.

Justifications must include mathematical reasons, not merely calculator results. Functions, graphs, tables, or other objects that are used in a justification should be clearly identified.

**Exploration Versus Mathematical Solution**

A graphing calculator is a powerful tool for exploration, but please remember that exploration is not a mathematical solution. Exploration with a graphing calculator can lead you toward an analytical solution, and after a solution is found, a graphing calculator can often be used to check the reasonableness of the solution.

**Note:** As on previous AP Calculus Exams, a decimal answer must be correct to three decimal places after the decimal point unless otherwise indicated. You should not round values in intermediate steps before a final answer is presented. And be aware that there are limitations inherent in graphing calculator technology; for example, answers obtained by tracing along a graph to find roots or points of intersection might not produce the required accuracy.